CN115452360B - Gear fault feature extraction method based on NA-MEMD and full vector spectrum - Google Patents
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Abstract
The invention discloses a gear fault feature extraction method based on NA-MEMD and full vector spectrum, which comprises the steps of collecting normal double-channel vibration signals, namely, double-channel vibration signals of gears with middle tooth missing faults, and 1) generating noise-containing normal double-channel vibration signals by adding Gaussian white noise to the collected signals; a dual-channel vibration signal of the noisy intermediate tooth-missing fault gear; 2) Processing the signals in the step 1) by NA-MEMD to obtain an Intrinsic Mode Function (IMF) group with the same frequency band corresponding number; 3) Selecting sensitive IMFs of the original signal from the IMF group by using a correlation coefficient criterion; 4) Performing Hilbert transform on the extracted sensitive IMF to obtain an envelope; 5) And finally, carrying out full vector information fusion on the envelope signals, drawing a full vector Hilbert spectrum, and realizing feature extraction of gear faults.
Description
Technical Field
The invention belongs to the field of gear fault diagnosis, and relates to a gear fault feature extraction method based on NA-MEMD and full vector spectrums.
Background
Gears are widely used in various transmission systems as key components in mechanical devices. As a key part of the transmission system, the speed, torque and direction of the input shaft can be changed through gears, so that the transmission system is widely applied to mechanical equipment in the fields of agriculture, transportation, aerospace and the like. Because gears generally operate in a relatively harsh environment, long-term operation can easily cause faults such as tooth surface wear, tooth breakage, contact fatigue, tooth surface gluing and the like of the gears. In severe cases, the whole mechanical system may fail, resulting in serious economic loss and even endangering the life health and safety of the staff. Therefore, aiming at the local weak faults existing in the early stage of the gear, the fault characteristics are extracted according to the vibration signals generated by the mutual meshing of the driving wheel and the driven wheel, the fault information of the gear is obtained early, and the method has very important significance for economically and reasonably arranging the time for maintaining the equipment and avoiding the occurrence of serious personal and equipment casualties.
The conventional gear fault feature extraction method is mostly from the perspective of time-frequency domain analysis, such as short-time fourier transform (STFT), wavelet transform and Empirical Mode Decomposition (EMD). Wherein EMD is an adaptive nonlinear non-stationary data analysis method, compared with wavelet transformation, the method does not need to select wavelet basis functions by oneself; however, the method is used for analyzing single-channel signals, and the single-channel signals are simply relied on, so that information omission is inevitably caused, the fault characteristics contained in the spectrogram obtained after time-frequency analysis are not obvious, and fault diagnosis cannot be carried out. Moreover, after EMD decomposition, there is often a problem of modal aliasing, affecting the subsequent spectral analysis. Also, empirical mode decomposition of multichannel signals also suffers from modal aliasing. After the multi-modal decomposition, a multi-element IMF group is generated, and how to select the IMF component with the most fault feature information plays a vital role in the subsequent extraction of the fault feature.
In addition, when the gear is in partial fault, periodic transient impact is generated, and the impact signal is modulated with an inherent vibration signal and a noise signal of the system to form a modulation signal. The signals generated by the local faults are weak relative to the system inherent vibration signals and noise signals, and are difficult to find.
Disclosure of Invention
The invention aims to provide a gear fault feature extraction method based on NA-MEMD and full vector spectrum, which realizes feature extraction of gear faults.
The technical solution for realizing the purpose of the invention is as follows:
a gear fault feature extraction method based on NA-MEMD and full vector spectrum comprises the following steps:
Step 1, setting sampling frequency, respectively acquiring normal double-channel vibration signals x 0(t)、y0 (t), and generating noise-containing normal double-channel vibration signals x 2(t)、y2 (t) by adding white Gaussian noise to the acquired signals, wherein the double-channel vibration signals x 1(t)、y1 (t) of gears with middle tooth missing faults occur; and a double-channel vibration signal x 3(t)、y3 (t) of the noisy middle tooth-missing fault gear, wherein t represents the number of sampling points.
Step 2, performing NA-MEMD processing on the signals to obtain a multi-element IMF group: all signals are formed into a multi-dimensional time sequence, the multi-dimensional signals are projected along a plurality of different directions respectively to obtain respective multi-directional vectors, the envelope signals of the multi-directional vectors of the corresponding signals are obtained, the average value is obtained, whether the result d (t) of subtracting the average value from the original signals meets the IMF condition is judged, if yes, d (t) is the first-order IMF component which is decomposed, the corresponding original signals are used for subtracting d (t) as new signals, and the solution of the envelope average value is continued to be carried out to screen the IMF component until the stopping criterion of the multi-element IMF is met; if not, d (t) is used as a new signal to continue to carry out the solution of the envelope mean value until the condition of IMF is met;
Step 3, screening IMF components with the most fault information in the IMF group corresponding to the fault gear dual-channel signal, namely sensitive IMF components, through calculating cross correlation coefficients between the IMF components obtained through decomposition and between the IMF components and the corresponding original signals;
Step 4, screening out sensitive IMF components IMF x,IMFy of a double-channel fault gear, respectively carrying out Hilbert transformation on IMF x,IMFy to obtain Hilbert transformation pairs, respectively taking Hilbert transformation pairs corresponding to IMF x,IMFy and IMF x,IMFy as a real part and an imaginary part of an analytic signal z x(t)、zy (t), and solving an envelope signal |z x(t)|、|zy (t) | of the analytic signal;
and 5, carrying out full vector information fusion on the obtained dual-channel envelope signal |z x(t)|、|zy (t) | of the fault gear, and carrying out fast Fourier transform, so as to obtain a full vector Hilbert spectrum, and finally, realizing the extraction and analysis of fault characteristics.
Compared with the prior art, the invention has the remarkable advantages that:
(1) According to the invention, NA-MEMD is used for carrying out self-adaptive decomposition on the gear double-channel vibration signals, so that the problem that fault information is omitted in single-channel vibration signal decomposition is solved. Meanwhile, in the decomposition process, a signal with a signal-to-noise ratio of 20db is added, so that the problem of modal aliasing existing in multi-element empirical mode decomposition is effectively restrained.
(2) The present invention calculates the coefficient of sensitivity by correlation coefficient criteria to select the most IMF component containing fault signature information. Through the calculation of the sensitivity coefficient, not only the correlation coefficient between the IMF component and the original signal is considered, but also the correlation coefficient between the fault IMF component and the normal IMF component in the same frequency band is considered, so that the IMF component with the most fault characteristic information is screened out.
(3) According to the invention, from an IMF group obtained after NA-MEMD processing, dual-channel sensitive IMFs of a fault gear are screened, hilbert transformation is firstly carried out on the dual-channel sensitive IMFs to obtain an envelope, then full vector information fusion is carried out on an envelope signal, and a full vector Hilbert spectrum is drawn. The full vector Hilbert spectrum combines the demodulation advantage of the Hilbert spectrum on the signals and the advantage of the full vector spectrum fusion multichannel information, and the gear fault characteristic frequency is successfully extracted. Under the same condition, compared with an envelope spectrum of a single channel signal and a spectrum obtained by multi-element empirical mode decomposition without noise assistance, the fault characteristics are more obvious.
Drawings
FIG. 1 is a basic flow chart of a method for extracting gear fault features based on NA-MEMD and full vector Hilbert spectra.
Fig. 2 is a full vector hilbert spectrum of a dual channel sensitive IMF for a failed gear.
Fig. 3 is a hilbert spectrum of a fault gear x-direction sensitive IMF.
Fig. 4 is a hilbert spectrum of a y-direction sensitive IMF of a faulty gear.
Fig. 5 is a full vector hilbert spectrum of a failed gear noiseless auxiliary channel sensitive IMF.
Detailed Description
The invention is further described with reference to the drawings and specific embodiments.
Referring to fig. 1,2,3, 4 and 5, the gear fault feature extraction method based on NA-MEMD and full vector spectrum in this embodiment specifically includes the following steps:
Step 1: the method comprises the steps of respectively acquiring normal double-channel vibration signals x 0(t)、y0 (t) at a sampling frequency of 50kHz, mutually perpendicular directions of two channels, generating a double-channel vibration signal x 1(t)、y1 (t) of a gear with middle tooth missing fault, and generating a noise-containing normal double-channel vibration signal x 2(t)、y2 (t) with a signal-to-noise ratio of 20dB by adding Gaussian white noise to the acquired signals; the signal-to-noise ratio is 20dB, the two-channel vibration signal x 3(t)、y3 (t) of the noisy middle missing tooth fault gear takes the signals as input signals, and the matrix gear transmission system consists of a large gear with the number of teeth of 200 and a small gear with the number of teeth of 20, wherein the small gear has middle missing tooth fault; the pinion is an input gear, the bull gear is an output gear, and the meshing frequency f m of the bull gear and the pinion is:
fm＝f1z1＝f2z2
where f 1 and f 2 represent the frequencies of rotation of the input gear and the output gear, and z 1 and z 2 represent the number of teeth of the input gear and the output gear. The motor speed for driving the input gear is 3200rpm, and the rotation frequency f 1 of the input gear is as follows:
Wherein n is the rotation speed of a motor for driving the driving gear to rotate, so that the rotation frequency f 1 of the input gear is 53.33Hz, the rotation frequency f 2 of the output gear is 5.33Hz, and the meshing frequency is 1066.67Hz.
Step 2: performing NA-MEMD processing on the signals to obtain a multi-element IMF group; the NA-MEMD treatment comprises the following specific processes:
(1) Constructing a multi-channel input signal matrix according to the input signals in the step 1:
X(t)＝{x0(t),y0(t),x1(t),y1(t),x2(t),y2(t),x3(t),y3(t)}
where t represents the number of sampling points.
(2) Adopting a low-difference HAMMERSLEY sequence sampling algorithm, selecting a group of uniformly distributed sampling point sets on a (w-1) dimensional sphere to generate a w-dimensional direction vector, wherein the dimension w of an input signal is=8
Where K represents the total number of projection directions, K represents the kth projection direction, v represents the v-th dimension of the input signal,The kth projection direction representing the nth dimension, θ k, is the direction angle of the corresponding direction vector, defining Wherein the method comprises the steps ofA direction angle representing the kth projection direction of the nth dimension.
(3) Calculating the projection of the multichannel input signal along each direction vector to obtain a projection set of K directions, which is recorded asDetermination ofAll extremum and time corresponding to extremumWherein i=1, 2, … t represents the i-th sampling point, and interpolation of extreme points is performed by using a multi-spline interpolation functionObtaining K multiple envelope signalsAnd calculating the average value of the envelopes of w channel signals on the K direction vectors of the spherical space:
(4) Judging whether the result d (t) of subtracting the average value from the original signal meets the IMF condition, if so, d (t) is the decomposed first-order IMF component, subtracting d (t) from a certain dimension signal in the input signal as a new signal, and continuing solving the envelope average value to screen the IMF component until the stopping criterion of the multi-element IMF is met; if not, d (t) is used as a new signal to continue to carry out the solution of the envelope mean value until the condition of IMF is met, and the IMF component corresponding to each dimension of input signal can be obtained by the same method.
(5) Repeating the steps until all signals meet the stopping criterion, and decomposing the w-channel multivariable signals into: Where p is the number of IMF components decomposed per channel, c i (t) and r (t) represent the IMF components and residuals for x (t).
Step 3: the sensitivity coefficient of each failed IMF component is calculated from the cross-correlation coefficients between IMF components and between the IMF components and the corresponding original signal. The method comprises the following steps:
(1) The correlation is a measure of the degree of linear correlation between variables, and for x 0(t),y0 (t) in the multi-channel input signal matrix, their correlation coefficients are:
Wherein the method comprises the steps of Representing the mean value of the sequence x 0(t),y0 (t) respectively,Represents the ith sample point of the sequence x 0 (t),Representing the ith sample point of sequence y 0 (t).
(2) Respectively calculating the correlation coefficient between the IMF component of the dual-channel vibration signal of the normal gear and the original signal, and calculating the average value, and marking the average value as Q n; respectively calculating the correlation coefficient between the IMF component of the dual-channel vibration signal of the middle tooth-missing fault gear and the original signal, calculating the average value, and recording as p n; and calculating correlation coefficients of the IMF components of the dual-channel vibration signals of the normal gear and the IMF components of the dual-channel vibration signals of the middle tooth missing fault gear respectively, and calculating the average value of the correlation coefficients, and recording the average value as T n.
(3) Calculating a sensitivity coefficient S n:
Wherein, Q n and P n represent the correlation degree of the multi-dimensional IMF component group obtained by NA-MEMD decomposition and the corresponding original signal, and the larger the value is, the more similar the original signal is; t n represents the degree of correlation between IMF components in different dimensions in the same frequency band, the smaller the value of which, the greater the IMF component variation. The larger the S n, the more sensitive the IMF component is to reflect the spectral change.
(4) According to the formula of the sensitivity coefficient in the step (3), the sensitivity coefficient of the dual-channel IMF group of the gear with the middle tooth missing fault is calculated as shown in the following table:
As can be seen from the above table, the first-order IMF has the greatest sensitivity coefficient, which means that the first-order IMF component contains the most fault information and can represent the original signal most.
Step 4: according to step 3, the sensitive IMF components of the two channels of the fault gear are screened as first-order IMF components, hilbert transformation is carried out on the first-order IMF components of the two channels respectively to obtain Hilbert transformation pairs of the first-order IMF components, the original signals and the Hilbert transformation pairs corresponding to the original signals are respectively used as real parts and imaginary parts of analytic signals z x(t)、zy (t), and an envelope signal |z x(t)|、|zy (t) | of the analytic signals is obtained.
Step 5: and carrying out full vector fusion on the Hilbert envelope signals of the two channels, and then carrying out spectrum analysis to obtain a spectrum which can obtain more information of the vibration signals. The global fusion algorithm is specifically as follows:
(1) Assuming that the gear is running smoothly, in the vibration signals with two channels perpendicular to each other, the obtained information of gear vibration will make steady-state whirl in the form of a combination of several harmonics ω a (a=1, 2 …), and the whirl track is a series of ellipses.
(2) Forming a complex sequence of z= |z x(t)|+j|zy (t) | by using the envelope signal |z x(t)|、|zy (t) | obtained in the step 4, wherein z=z R+ZI is obtained through fourier transformation, and Z R and Z I are respectively a real part and an imaginary part of Z;
(3) The major axis of the ellipse is defined as the dominant vibration vector, and the dominant vibration vector at a certain frequency is generally used to represent the vibration intensity at that frequency. Wherein the main vibration vector R is:
Wherein the method comprises the steps of As half of the total number of sampling points t, |z u | represents the first half of the fourier transform of the envelope signal, and |z t-u | represents the second half of the fourier transform of the envelope signal.
(4) According to Hilbert envelope demodulation and full vector fusion algorithm, the full vector Hilbert spectrum of the fault gear sensitive IMF is drawn as shown in figure 2, and as known from step 1, the rotation frequency of the fault gear is 53.33Hz, and when the gear breaks down, the vibration signal of the fault gear can generate the fault gear rotation frequency and the high-order frequency multiplication thereof in the frequency domain. In fig. 2 we can clearly observe the failure frequency 50.68Hz and its higher order multiples 101.36Hz, 152.32Hz, 203Hz and 254.79Hz.
(5) According to Hilbert envelope demodulation, an envelope spectrum of a single channel of a fault gear is drawn, as shown in fig. 3 and 4, in an x-direction envelope spectrum, the frequency conversion 50.68Hz and the frequency multiplication 101.36Hz of the fault gear can be clearly seen, and in a y-direction envelope spectrum, the high-order frequency multiplication 152.32Hz, 203Hz and 254.79Hz of the rotation frequency of the fault gear can be clearly seen, but the frequency conversion and the first-order frequency multiplication are submerged by side bands. Comparing fig. 2,3 and 4, it can be seen that although the envelope spectrum of a single channel can also extract the fault characteristics of the fault gear, the problem of information omission exists, and the full vector hilbert spectrum fuses the fault information of the double channels, so that the fault characteristics are more obvious.
(6) When the NA-MEMD is used for decomposing the multi-element signals, no noise signal is added, the full vector hilbert spectrum of the sensitive IMF of the fault gear is drawn as shown in fig. 5, and comparing fig. 1 and 5, it can be known that when the multi-element empirical mode decomposition is performed in fig. 5, no noise assistance is added, and mode aliasing exists, so that the amplitude of the full vector hilbert spectrum of the finally drawn sensitive IMF is lower than the amplitude of the frequency corresponding to the full vector hilbert spectrum in fig. 2, which is unfavorable for the extraction of fault characteristics.
In conclusion, the method can effectively solve the problems that the characteristics of weak fault signals at the early stage of the gear are not suitable to be extracted, and fault information is easy to lose in single-channel signal analysis, and has excellent performance in the same-field diagnosis method, obvious extracted fault characteristics and wide application prospects in the field of gear rotation and other rotary machinery fault diagnosis.
Claims (5)
1. A gear fault feature extraction method based on NA-MEMD and full vector spectrum is characterized in that: the method comprises the following steps:
Step 1, setting sampling frequency, respectively acquiring normal double-channel vibration signals x 0(t)、y0 (t), and generating noise-containing normal double-channel vibration signals x 2(t)、y2 (t) by adding white Gaussian noise to the acquired signals, wherein the double-channel vibration signals x 1(t)、y1 (t) of gears with middle tooth missing faults occur; a double-channel vibration signal x 3(t)、y3 (t) of the noisy intermediate tooth-missing fault gear, wherein t represents the number of sampling points;
Step 2, performing NA-MEMD processing on the signals to obtain a multi-element IMF group: all signals are formed into a multi-dimensional time sequence, the multi-dimensional signals are projected along a plurality of different directions respectively to obtain respective multi-directional vectors, the envelope signals of the multi-directional vectors of the corresponding signals are obtained, the average value is obtained, whether the result d (t) of subtracting the average value from the original signals meets the IMF condition is judged, if yes, d (t) is the first-order IMF component which is decomposed, the corresponding original signals are used for subtracting d (t) as new signals, and the solution of the envelope average value is continued to be carried out to screen the IMF component until the stopping criterion of the multi-element IMF is met; if not, d (t) is used as a new signal to continue to carry out the solution of the envelope mean value until the condition of IMF is met;
Step 3, screening IMF components with the most fault information in the IMF group corresponding to the fault gear dual-channel signal, namely sensitive IMF components, through calculating cross correlation coefficients between the IMF components obtained through decomposition and between the IMF components and the corresponding original signals;
Step 4, screening out sensitive IMF components IMF x,IMFy of a double-channel fault gear, respectively carrying out Hilbert transformation on IMF x,IMFy to obtain Hilbert transformation pairs, respectively taking Hilbert transformation pairs corresponding to IMF x,IMFy and IMF x,IMFy as a real part and an imaginary part of an analytic signal z x(t)、zy (t), and solving an envelope signal |z x(t)|、|zy (t) | of the analytic signal;
and 5, carrying out full vector information fusion on the obtained dual-channel envelope signal |z x(t)|、|zy (t) | of the fault gear, and carrying out fast Fourier transform, so as to obtain a full vector Hilbert spectrum, and finally, realizing the extraction and analysis of fault characteristics.
2. The gear fault feature extraction method based on NA-MEMD and full vector spectrum according to claim 1, wherein step 2 is to calculate IMF component group, and the specific steps are as follows:
(1) Building a multi-channel input signal matrix:
X(t)＝{x0(t),y0(T),x1(t),y1(t),x2(t),y2(t),x3(t),y3(t)}
Wherein t represents the number of sampling points;
(2) Adopting a low-difference HAMMERSLEY sequence sampling algorithm to select a group of uniformly distributed sampling point sets on the w-1-dimensional spherical surface to generate a w-dimensional direction vector
Where K represents the total number of projection directions, K represents the kth projection direction, v represents the v-th dimension of the input signal,The kth projection direction representing the nth dimension, θ k, is the direction angle of the corresponding direction vector, defining Wherein the method comprises the steps ofA direction angle representing a kth projection direction of a nth dimension;
(3) Calculating the projection of the multichannel input signal along each direction vector to obtain a projection set of K directions, which is recorded as Determination ofAll extremum and time corresponding to extremumWherein i=1, 2, … t represents the i-th sampling point, and interpolation of extreme points is performed by using a multi-spline interpolation functionObtaining K multiple envelope signalsAnd calculating the average value of the envelopes of w channel signals on the K direction vectors of the spherical space:
(4) Judging whether the result d (t) of subtracting the average value from the original signal meets the IMF condition or not to obtain IMF components corresponding to each dimension of input signals;
(5) Repeating the steps until all signals meet the stopping criterion, and decomposing the w-channel multivariable signals into: Where p is the number of IMF components decomposed per channel, c i (t) and r (t) represent the IMF components and residuals for x (t).
3. The NA-MEMD and full spectrum based gear fault feature extraction method according to claim 1, wherein the sensitivity coefficient S n:
Wherein Q n is the correlation coefficient of the IMF component of the dual-channel vibration signal of the normal gear and the original signal, p n is the correlation coefficient of the IMF component of the dual-channel vibration signal of the middle tooth missing fault gear and the original signal, and T n is the correlation coefficient of the IMF component of the dual-channel vibration signal of the normal gear and the IMF component of the dual-channel vibration signal of the middle tooth missing fault gear respectively.
4. The gear fault feature extraction method based on NA-MEMD and full vector spectrum according to claim 1, wherein the full vector fusion algorithm is specifically as follows:
1) Assuming that the running of the gear is stable, in the vibration signals with the two channel directions being perpendicular to each other, the obtained information of the vibration of the gear is subjected to steady state whirling in a combination form of a plurality of harmonic waves, and a whirling track is a series of ellipses;
2) The envelope signal |z x(t)|、|zy (t) | constitutes a complex sequence z= |z x(t)|+j|zy (t) |, with z=z R+ZI by fourier transform, where Z R and Z I are the real and imaginary parts of Z, respectively;
3) The major axis of the ellipse is defined as the dominant vibration vector, and the dominant vibration vector at a certain frequency is used to represent the vibration intensity at that frequency.
5. The NA-MEMD and full spectrum based gear fault feature extraction method of claim 4, wherein the principal vibration vector R is:
Wherein the method comprises the steps of As half of the total number of sampling points t, |z u | represents the first half of the fourier transform of the envelope signal, and |z t-u | represents the second half of the fourier transform of the envelope signal.
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